Source file src/crypto/elliptic/elliptic_test.go

     1  // Copyright 2010 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package elliptic
     6  
     7  import (
     8  	"bytes"
     9  	"crypto/rand"
    10  	"encoding/hex"
    11  	"math/big"
    12  	"testing"
    13  )
    14  
    15  // genericParamsForCurve returns the dereferenced CurveParams for
    16  // the specified curve. This is used to avoid the logic for
    17  // upgrading a curve to its specific implementation, forcing
    18  // usage of the generic implementation.
    19  func genericParamsForCurve(c Curve) *CurveParams {
    20  	d := *(c.Params())
    21  	return &d
    22  }
    23  
    24  func testAllCurves(t *testing.T, f func(*testing.T, Curve)) {
    25  	tests := []struct {
    26  		name  string
    27  		curve Curve
    28  	}{
    29  		{"P256", P256()},
    30  		{"P256/Params", genericParamsForCurve(P256())},
    31  		{"P224", P224()},
    32  		{"P224/Params", genericParamsForCurve(P224())},
    33  		{"P384", P384()},
    34  		{"P384/Params", genericParamsForCurve(P384())},
    35  		{"P521", P521()},
    36  		{"P521/Params", genericParamsForCurve(P521())},
    37  	}
    38  	if testing.Short() {
    39  		tests = tests[:1]
    40  	}
    41  	for _, test := range tests {
    42  		curve := test.curve
    43  		t.Run(test.name, func(t *testing.T) {
    44  			t.Parallel()
    45  			f(t, curve)
    46  		})
    47  	}
    48  }
    49  
    50  func TestOnCurve(t *testing.T) {
    51  	testAllCurves(t, func(t *testing.T, curve Curve) {
    52  		if !curve.IsOnCurve(curve.Params().Gx, curve.Params().Gy) {
    53  			t.Error("basepoint is not on the curve")
    54  		}
    55  	})
    56  }
    57  
    58  func TestOffCurve(t *testing.T) {
    59  	testAllCurves(t, func(t *testing.T, curve Curve) {
    60  		x, y := new(big.Int).SetInt64(1), new(big.Int).SetInt64(1)
    61  		if curve.IsOnCurve(x, y) {
    62  			t.Errorf("point off curve is claimed to be on the curve")
    63  		}
    64  
    65  		byteLen := (curve.Params().BitSize + 7) / 8
    66  		b := make([]byte, 1+2*byteLen)
    67  		b[0] = 4 // uncompressed point
    68  		x.FillBytes(b[1 : 1+byteLen])
    69  		y.FillBytes(b[1+byteLen : 1+2*byteLen])
    70  
    71  		x1, y1 := Unmarshal(curve, b)
    72  		if x1 != nil || y1 != nil {
    73  			t.Errorf("unmarshaling a point not on the curve succeeded")
    74  		}
    75  	})
    76  }
    77  
    78  func TestInfinity(t *testing.T) {
    79  	testAllCurves(t, testInfinity)
    80  }
    81  
    82  func isInfinity(x, y *big.Int) bool {
    83  	return x.Sign() == 0 && y.Sign() == 0
    84  }
    85  
    86  func testInfinity(t *testing.T, curve Curve) {
    87  	x0, y0 := new(big.Int), new(big.Int)
    88  	xG, yG := curve.Params().Gx, curve.Params().Gy
    89  
    90  	if !isInfinity(curve.ScalarMult(xG, yG, curve.Params().N.Bytes())) {
    91  		t.Errorf("x^q != ∞")
    92  	}
    93  	if !isInfinity(curve.ScalarMult(xG, yG, []byte{0})) {
    94  		t.Errorf("x^0 != ∞")
    95  	}
    96  
    97  	if !isInfinity(curve.ScalarMult(x0, y0, []byte{1, 2, 3})) {
    98  		t.Errorf("∞^k != ∞")
    99  	}
   100  	if !isInfinity(curve.ScalarMult(x0, y0, []byte{0})) {
   101  		t.Errorf("∞^0 != ∞")
   102  	}
   103  
   104  	if !isInfinity(curve.ScalarBaseMult(curve.Params().N.Bytes())) {
   105  		t.Errorf("b^q != ∞")
   106  	}
   107  	if !isInfinity(curve.ScalarBaseMult([]byte{0})) {
   108  		t.Errorf("b^0 != ∞")
   109  	}
   110  
   111  	if !isInfinity(curve.Double(x0, y0)) {
   112  		t.Errorf("2∞ != ∞")
   113  	}
   114  	// There is no other point of order two on the NIST curves (as they have
   115  	// cofactor one), so Double can't otherwise return the point at infinity.
   116  
   117  	nMinusOne := new(big.Int).Sub(curve.Params().N, big.NewInt(1))
   118  	x, y := curve.ScalarMult(xG, yG, nMinusOne.Bytes())
   119  	x, y = curve.Add(x, y, xG, yG)
   120  	if !isInfinity(x, y) {
   121  		t.Errorf("x^(q-1) + x != ∞")
   122  	}
   123  	x, y = curve.Add(xG, yG, x0, y0)
   124  	if x.Cmp(xG) != 0 || y.Cmp(yG) != 0 {
   125  		t.Errorf("x+∞ != x")
   126  	}
   127  	x, y = curve.Add(x0, y0, xG, yG)
   128  	if x.Cmp(xG) != 0 || y.Cmp(yG) != 0 {
   129  		t.Errorf("∞+x != x")
   130  	}
   131  
   132  	if curve.IsOnCurve(x0, y0) {
   133  		t.Errorf("IsOnCurve(∞) == true")
   134  	}
   135  
   136  	if xx, yy := Unmarshal(curve, Marshal(curve, x0, y0)); xx != nil || yy != nil {
   137  		t.Errorf("Unmarshal(Marshal(∞)) did not return an error")
   138  	}
   139  	// We don't test UnmarshalCompressed(MarshalCompressed(∞)) because there are
   140  	// two valid points with x = 0.
   141  	if xx, yy := Unmarshal(curve, []byte{0x00}); xx != nil || yy != nil {
   142  		t.Errorf("Unmarshal(∞) did not return an error")
   143  	}
   144  	byteLen := (curve.Params().BitSize + 7) / 8
   145  	buf := make([]byte, byteLen*2+1)
   146  	buf[0] = 4 // Uncompressed format.
   147  	if xx, yy := Unmarshal(curve, buf); xx != nil || yy != nil {
   148  		t.Errorf("Unmarshal((0,0)) did not return an error")
   149  	}
   150  }
   151  
   152  func TestMarshal(t *testing.T) {
   153  	testAllCurves(t, func(t *testing.T, curve Curve) {
   154  		_, x, y, err := GenerateKey(curve, rand.Reader)
   155  		if err != nil {
   156  			t.Fatal(err)
   157  		}
   158  		serialized := Marshal(curve, x, y)
   159  		xx, yy := Unmarshal(curve, serialized)
   160  		if xx == nil {
   161  			t.Fatal("failed to unmarshal")
   162  		}
   163  		if xx.Cmp(x) != 0 || yy.Cmp(y) != 0 {
   164  			t.Fatal("unmarshal returned different values")
   165  		}
   166  	})
   167  }
   168  
   169  func TestUnmarshalToLargeCoordinates(t *testing.T) {
   170  	// See https://golang.org/issues/20482.
   171  	testAllCurves(t, testUnmarshalToLargeCoordinates)
   172  }
   173  
   174  func testUnmarshalToLargeCoordinates(t *testing.T, curve Curve) {
   175  	p := curve.Params().P
   176  	byteLen := (p.BitLen() + 7) / 8
   177  
   178  	// Set x to be greater than curve's parameter P – specifically, to P+5.
   179  	// Set y to mod_sqrt(x^3 - 3x + B)) so that (x mod P = 5 , y) is on the
   180  	// curve.
   181  	x := new(big.Int).Add(p, big.NewInt(5))
   182  	y := curve.Params().polynomial(x)
   183  	y.ModSqrt(y, p)
   184  
   185  	invalid := make([]byte, byteLen*2+1)
   186  	invalid[0] = 4 // uncompressed encoding
   187  	x.FillBytes(invalid[1 : 1+byteLen])
   188  	y.FillBytes(invalid[1+byteLen:])
   189  
   190  	if X, Y := Unmarshal(curve, invalid); X != nil || Y != nil {
   191  		t.Errorf("Unmarshal accepts invalid X coordinate")
   192  	}
   193  
   194  	if curve == p256 {
   195  		// This is a point on the curve with a small y value, small enough that
   196  		// we can add p and still be within 32 bytes.
   197  		x, _ = new(big.Int).SetString("31931927535157963707678568152204072984517581467226068221761862915403492091210", 10)
   198  		y, _ = new(big.Int).SetString("5208467867388784005506817585327037698770365050895731383201516607147", 10)
   199  		y.Add(y, p)
   200  
   201  		if p.Cmp(y) > 0 || y.BitLen() != 256 {
   202  			t.Fatal("y not within expected range")
   203  		}
   204  
   205  		// marshal
   206  		x.FillBytes(invalid[1 : 1+byteLen])
   207  		y.FillBytes(invalid[1+byteLen:])
   208  
   209  		if X, Y := Unmarshal(curve, invalid); X != nil || Y != nil {
   210  			t.Errorf("Unmarshal accepts invalid Y coordinate")
   211  		}
   212  	}
   213  }
   214  
   215  // TestInvalidCoordinates tests big.Int values that are not valid field elements
   216  // (negative or bigger than P). They are expected to return false from
   217  // IsOnCurve, all other behavior is undefined.
   218  func TestInvalidCoordinates(t *testing.T) {
   219  	testAllCurves(t, testInvalidCoordinates)
   220  }
   221  
   222  func testInvalidCoordinates(t *testing.T, curve Curve) {
   223  	checkIsOnCurveFalse := func(name string, x, y *big.Int) {
   224  		if curve.IsOnCurve(x, y) {
   225  			t.Errorf("IsOnCurve(%s) unexpectedly returned true", name)
   226  		}
   227  	}
   228  
   229  	p := curve.Params().P
   230  	_, x, y, _ := GenerateKey(curve, rand.Reader)
   231  	xx, yy := new(big.Int), new(big.Int)
   232  
   233  	// Check if the sign is getting dropped.
   234  	xx.Neg(x)
   235  	checkIsOnCurveFalse("-x, y", xx, y)
   236  	yy.Neg(y)
   237  	checkIsOnCurveFalse("x, -y", x, yy)
   238  
   239  	// Check if negative values are reduced modulo P.
   240  	xx.Sub(x, p)
   241  	checkIsOnCurveFalse("x-P, y", xx, y)
   242  	yy.Sub(y, p)
   243  	checkIsOnCurveFalse("x, y-P", x, yy)
   244  
   245  	// Check if positive values are reduced modulo P.
   246  	xx.Add(x, p)
   247  	checkIsOnCurveFalse("x+P, y", xx, y)
   248  	yy.Add(y, p)
   249  	checkIsOnCurveFalse("x, y+P", x, yy)
   250  
   251  	// Check if the overflow is dropped.
   252  	xx.Add(x, new(big.Int).Lsh(big.NewInt(1), 535))
   253  	checkIsOnCurveFalse("x+2⁵³⁵, y", xx, y)
   254  	yy.Add(y, new(big.Int).Lsh(big.NewInt(1), 535))
   255  	checkIsOnCurveFalse("x, y+2⁵³⁵", x, yy)
   256  
   257  	// Check if P is treated like zero (if possible).
   258  	// y^2 = x^3 - 3x + B
   259  	// y = mod_sqrt(x^3 - 3x + B)
   260  	// y = mod_sqrt(B) if x = 0
   261  	// If there is no modsqrt, there is no point with x = 0, can't test x = P.
   262  	if yy := new(big.Int).ModSqrt(curve.Params().B, p); yy != nil {
   263  		if !curve.IsOnCurve(big.NewInt(0), yy) {
   264  			t.Fatal("(0, mod_sqrt(B)) is not on the curve?")
   265  		}
   266  		checkIsOnCurveFalse("P, y", p, yy)
   267  	}
   268  }
   269  
   270  func TestMarshalCompressed(t *testing.T) {
   271  	t.Run("P-256/03", func(t *testing.T) {
   272  		data, _ := hex.DecodeString("031e3987d9f9ea9d7dd7155a56a86b2009e1e0ab332f962d10d8beb6406ab1ad79")
   273  		x, _ := new(big.Int).SetString("13671033352574878777044637384712060483119675368076128232297328793087057702265", 10)
   274  		y, _ := new(big.Int).SetString("66200849279091436748794323380043701364391950689352563629885086590854940586447", 10)
   275  		testMarshalCompressed(t, P256(), x, y, data)
   276  	})
   277  	t.Run("P-256/02", func(t *testing.T) {
   278  		data, _ := hex.DecodeString("021e3987d9f9ea9d7dd7155a56a86b2009e1e0ab332f962d10d8beb6406ab1ad79")
   279  		x, _ := new(big.Int).SetString("13671033352574878777044637384712060483119675368076128232297328793087057702265", 10)
   280  		y, _ := new(big.Int).SetString("49591239931264812013903123569363872165694192725937750565648544718012157267504", 10)
   281  		testMarshalCompressed(t, P256(), x, y, data)
   282  	})
   283  
   284  	t.Run("Invalid", func(t *testing.T) {
   285  		data, _ := hex.DecodeString("02fd4bf61763b46581fd9174d623516cf3c81edd40e29ffa2777fb6cb0ae3ce535")
   286  		X, Y := UnmarshalCompressed(P256(), data)
   287  		if X != nil || Y != nil {
   288  			t.Error("expected an error for invalid encoding")
   289  		}
   290  	})
   291  
   292  	if testing.Short() {
   293  		t.Skip("skipping other curves on short test")
   294  	}
   295  
   296  	testAllCurves(t, func(t *testing.T, curve Curve) {
   297  		_, x, y, err := GenerateKey(curve, rand.Reader)
   298  		if err != nil {
   299  			t.Fatal(err)
   300  		}
   301  		testMarshalCompressed(t, curve, x, y, nil)
   302  	})
   303  
   304  }
   305  
   306  func testMarshalCompressed(t *testing.T, curve Curve, x, y *big.Int, want []byte) {
   307  	if !curve.IsOnCurve(x, y) {
   308  		t.Fatal("invalid test point")
   309  	}
   310  	got := MarshalCompressed(curve, x, y)
   311  	if want != nil && !bytes.Equal(got, want) {
   312  		t.Errorf("got unexpected MarshalCompressed result: got %x, want %x", got, want)
   313  	}
   314  
   315  	X, Y := UnmarshalCompressed(curve, got)
   316  	if X == nil || Y == nil {
   317  		t.Fatalf("UnmarshalCompressed failed unexpectedly")
   318  	}
   319  
   320  	if !curve.IsOnCurve(X, Y) {
   321  		t.Error("UnmarshalCompressed returned a point not on the curve")
   322  	}
   323  	if X.Cmp(x) != 0 || Y.Cmp(y) != 0 {
   324  		t.Errorf("point did not round-trip correctly: got (%v, %v), want (%v, %v)", X, Y, x, y)
   325  	}
   326  }
   327  
   328  func TestLargeIsOnCurve(t *testing.T) {
   329  	testAllCurves(t, func(t *testing.T, curve Curve) {
   330  		large := big.NewInt(1)
   331  		large.Lsh(large, 1000)
   332  		if curve.IsOnCurve(large, large) {
   333  			t.Errorf("(2^1000, 2^1000) is reported on the curve")
   334  		}
   335  	})
   336  }
   337  
   338  func benchmarkAllCurves(b *testing.B, f func(*testing.B, Curve)) {
   339  	tests := []struct {
   340  		name  string
   341  		curve Curve
   342  	}{
   343  		{"P256", P256()},
   344  		{"P224", P224()},
   345  		{"P384", P384()},
   346  		{"P521", P521()},
   347  	}
   348  	for _, test := range tests {
   349  		curve := test.curve
   350  		b.Run(test.name, func(b *testing.B) {
   351  			f(b, curve)
   352  		})
   353  	}
   354  }
   355  
   356  func BenchmarkScalarBaseMult(b *testing.B) {
   357  	benchmarkAllCurves(b, func(b *testing.B, curve Curve) {
   358  		priv, _, _, _ := GenerateKey(curve, rand.Reader)
   359  		b.ReportAllocs()
   360  		b.ResetTimer()
   361  		for i := 0; i < b.N; i++ {
   362  			x, _ := curve.ScalarBaseMult(priv)
   363  			// Prevent the compiler from optimizing out the operation.
   364  			priv[0] ^= byte(x.Bits()[0])
   365  		}
   366  	})
   367  }
   368  
   369  func BenchmarkScalarMult(b *testing.B) {
   370  	benchmarkAllCurves(b, func(b *testing.B, curve Curve) {
   371  		_, x, y, _ := GenerateKey(curve, rand.Reader)
   372  		priv, _, _, _ := GenerateKey(curve, rand.Reader)
   373  		b.ReportAllocs()
   374  		b.ResetTimer()
   375  		for i := 0; i < b.N; i++ {
   376  			x, y = curve.ScalarMult(x, y, priv)
   377  		}
   378  	})
   379  }
   380  
   381  func BenchmarkMarshalUnmarshal(b *testing.B) {
   382  	benchmarkAllCurves(b, func(b *testing.B, curve Curve) {
   383  		_, x, y, _ := GenerateKey(curve, rand.Reader)
   384  		b.Run("Uncompressed", func(b *testing.B) {
   385  			b.ReportAllocs()
   386  			for i := 0; i < b.N; i++ {
   387  				buf := Marshal(curve, x, y)
   388  				xx, yy := Unmarshal(curve, buf)
   389  				if xx.Cmp(x) != 0 || yy.Cmp(y) != 0 {
   390  					b.Error("Unmarshal output different from Marshal input")
   391  				}
   392  			}
   393  		})
   394  		b.Run("Compressed", func(b *testing.B) {
   395  			b.ReportAllocs()
   396  			for i := 0; i < b.N; i++ {
   397  				buf := MarshalCompressed(curve, x, y)
   398  				xx, yy := UnmarshalCompressed(curve, buf)
   399  				if xx.Cmp(x) != 0 || yy.Cmp(y) != 0 {
   400  					b.Error("Unmarshal output different from Marshal input")
   401  				}
   402  			}
   403  		})
   404  	})
   405  }
   406  

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